LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ slasd3()

subroutine slasd3 ( integer nl,
integer nr,
integer sqre,
integer k,
real, dimension( * ) d,
real, dimension( ldq, * ) q,
integer ldq,
real, dimension( * ) dsigma,
real, dimension( ldu, * ) u,
integer ldu,
real, dimension( ldu2, * ) u2,
integer ldu2,
real, dimension( ldvt, * ) vt,
integer ldvt,
real, dimension( ldvt2, * ) vt2,
integer ldvt2,
integer, dimension( * ) idxc,
integer, dimension( * ) ctot,
real, dimension( * ) z,
integer info )

SLASD3 finds all square roots of the roots of the secular equation, as defined by the values in D and Z, and then updates the singular vectors by matrix multiplication. Used by sbdsdc.

Download SLASD3 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> SLASD3 finds all the square roots of the roots of the secular
!> equation, as defined by the values in D and Z.  It makes the
!> appropriate calls to SLASD4 and then updates the singular
!> vectors by matrix multiplication.
!>
!> SLASD3 is called from SLASD1.
!>
Parameters
[in]NL
!>          NL is INTEGER
!>         The row dimension of the upper block.  NL >= 1.
!>
[in]NR
!>          NR is INTEGER
!>         The row dimension of the lower block.  NR >= 1.
!>
[in]SQRE
!>          SQRE is INTEGER
!>         = 0: the lower block is an NR-by-NR square matrix.
!>         = 1: the lower block is an NR-by-(NR+1) rectangular matrix.
!>
!>         The bidiagonal matrix has N = NL + NR + 1 rows and
!>         M = N + SQRE >= N columns.
!>
[in]K
!>          K is INTEGER
!>         The size of the secular equation, 1 =< K = < N.
!>
[out]D
!>          D is REAL array, dimension(K)
!>         On exit the square roots of the roots of the secular equation,
!>         in ascending order.
!>
[out]Q
!>          Q is REAL array, dimension (LDQ,K)
!>
[in]LDQ
!>          LDQ is INTEGER
!>         The leading dimension of the array Q.  LDQ >= K.
!>
[in]DSIGMA
!>          DSIGMA is REAL array, dimension(K)
!>         The first K elements of this array contain the old roots
!>         of the deflated updating problem.  These are the poles
!>         of the secular equation.
!>
[out]U
!>          U is REAL array, dimension (LDU, N)
!>         The last N - K columns of this matrix contain the deflated
!>         left singular vectors.
!>
[in]LDU
!>          LDU is INTEGER
!>         The leading dimension of the array U.  LDU >= N.
!>
[in]U2
!>          U2 is REAL array, dimension (LDU2, N)
!>         The first K columns of this matrix contain the non-deflated
!>         left singular vectors for the split problem.
!>
[in]LDU2
!>          LDU2 is INTEGER
!>         The leading dimension of the array U2.  LDU2 >= N.
!>
[out]VT
!>          VT is REAL array, dimension (LDVT, M)
!>         The last M - K columns of VT**T contain the deflated
!>         right singular vectors.
!>
[in]LDVT
!>          LDVT is INTEGER
!>         The leading dimension of the array VT.  LDVT >= N.
!>
[in,out]VT2
!>          VT2 is REAL array, dimension (LDVT2, N)
!>         The first K columns of VT2**T contain the non-deflated
!>         right singular vectors for the split problem.
!>
[in]LDVT2
!>          LDVT2 is INTEGER
!>         The leading dimension of the array VT2.  LDVT2 >= N.
!>
[in]IDXC
!>          IDXC is INTEGER array, dimension (N)
!>         The permutation used to arrange the columns of U (and rows of
!>         VT) into three groups:  the first group contains non-zero
!>         entries only at and above (or before) NL +1; the second
!>         contains non-zero entries only at and below (or after) NL+2;
!>         and the third is dense. The first column of U and the row of
!>         VT are treated separately, however.
!>
!>         The rows of the singular vectors found by SLASD4
!>         must be likewise permuted before the matrix multiplies can
!>         take place.
!>
[in]CTOT
!>          CTOT is INTEGER array, dimension (4)
!>         A count of the total number of the various types of columns
!>         in U (or rows in VT), as described in IDXC. The fourth column
!>         type is any column which has been deflated.
!>
[in,out]Z
!>          Z is REAL array, dimension (K)
!>         The first K elements of this array contain the components
!>         of the deflation-adjusted updating row vector.
!>
[out]INFO
!>          INFO is INTEGER
!>         = 0:  successful exit.
!>         < 0:  if INFO = -i, the i-th argument had an illegal value.
!>         > 0:  if INFO = 1, a singular value did not converge
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA